Use a graphing utility to graph the region bounded by the graphs of the equations. Then find the area of the region analytically. y =(1/ 10)xe3x, y = 0, x = 0, x = 2

Q: Find the area of the given region. Use a graphing utility to verify your result.

A: the given graph of the function y=4ex1+e2x is: we have to find the area of the given region.  we…

Q: Use a graphing utility to find the intersection points of the curves, and then use the utility to…

A: y=5-x-22, y=ex Use the graphing calculator to draw the graph and mentioned the intersection point.

Q: Find the area of the given region. Use a graphing utility to verify your result. 1+ In x3 y y 1 4

A: we have to find area

Q: Find the area of the region bounded by the curves below. Sketch its graph and shade the region. 1.…

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Q: Find the area of the given region. Use a graphing utility to verify your result.

A: Given: To find: The area of the given region.

Q: Find the area of the region bounded by the graphs of the equations.

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Q: Sketch the region bounded by the graphs of the equations and find the area of the region    y= csc…

A: Given y = csc(x), y=2, π/6 ≤ x ≤ 5π/6

Q: a) Sketch the region enclosed by the curves y = 12 – x², y = x² – 20. - - b) Find the area of the…

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Q: Sketch the region enclosed by y = 4x and Y = 4x. Find the area of the region.

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Q: Find the area of the region bounded by the graphs of the equations. y = 1+√√x, x=0, x= 8, y = 0…

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Q: Find the area of the region bounded by the graphs of the equations: x = 4 – y? x = y – 2

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Q: Find the area of the region bounded by the graphs of the equations. а. у %3D 5x2 + 2, х%3D0, х%3D2,…

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Q: In the question  given follows,use a graphing utility to graph the region bounded by the graphs of…

A: Find the region bounded by the graphs y=110xe3x, y=0, x=0, x=2. Plot the region bounded by the…

Q: Find the area of the given region. Use a graphing utility to verify your result. 1 + In x3 y = y 1 2…

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Q: Determine the area of the given region. The region bounded by y = x2, y = 2x2 - 4x, and y = 0

A: Given, The curves are y = x2, y = 2x2 - 4x, and y = 0 The graph of the region is as below

Q: Find the area between y=x2-x2 and y=x2. Sketch the region

A: The given curves are: y=2-x2    and    y=x2

Q: Draw the figure showing the region and find the area of the region bounded by the curves. y 4 - х?;…

A: Area is calculated with the help of double and single integral. In case of single integral function…

Q: 3. Sketch the region enclosed by the curves y=-x +3x and y = x. Hence, find the area of the region.

A: We have to find the area

Q: Sketch the region enclosed by the given curves. y = Vx- 3, x- y = 3 2 3 1 3 4 -2 Find the area of…

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Q: Find the area of the region described. The region bounded by y = (x-6) and y 2x- 12

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Q: Find the area between y=x4-x2 and y=x2 . Sketch the region

A: given  y=x4-x2 and y=x2 intersection  x4-x2=x2x4-2x2=0x2(x2-2)=0x2=0   or x2-2=0x=0    or x2=2x=0…

Q: Sketch the region enclosed by the curves y=x+2, y=25-x^2, x=-2, and x=2. Find the area of the…

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Q: Find the area between y= x4-x2  and y=  x2 Sketch the region

A: Solve by integration

Q: Find the area of the given region. Use a graphing utility to verify your result.

A: Given: y=1+lnx3x

Q: y = x² ; y = 8 – x²; 4x – y + 12 = 0

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Q: Find the area bounded by y=(1-x^2)^2 and y=0   Solve by drawing a figure to show the bounded…

A: From the given curve the bounded region is shown below:     Now using the double integral method to…

Q: Sketch the region bounded by the graphs of the equations and find the area of the region. x = y2 −…

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Q: Find the area of the region bounded by the graphs of the equations. y = -x2 + 2x, y = 0 Submit…

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Q: Determine the area of the given region. The region bounded by y = 2x2 - 6x + 5 and y = 1

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Q: Find the area between y = x* - x² and y = x². Sketch the region.

A: You have posted multiple questions. As per the instruction, we will be answering only the first…

Q: 3x 4x e, y = e", and Sketch the region enclosed by y = x = 1. Find the area of the region.

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Q: Find the area of the region bounded by the graphs of the equations. y = x - x°, x = 0, x = 1, y = 0…

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Q: Sketch the region bounded by the graphs of the equations and find the area of the region y = x, y =…

A: We sketch the region using a graphing calculator

Q: Draw the figure showing the region and find the area of the region bounded by the curves. y = 4x –…

A: Area of the region is obtained by definite integral . There are two ways of finding area , first…

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A: Given problem:- Sketch the region enclosed by the given curves. Decide whether to integrate with…

Q: Find the area of the given region. Use a graphing utility to verify your result. 1 + In x3 y = y 1 1…

A: The region bounded by y=1+ln x3x between x=1 to x=2

Q: Find the area of the given region. Use a graphing utility to verify your 1 + In x3 y = y 1 X. 1 3 4…

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Q: Given the region bounded by the graphs below, find the area of the plane region. x=y^2+1, x=0,…

A: Given that x=y^2+1, x=0, y=-1, y=2 To find the area of the plane region

Q: Sketch the region between y = x2 + a - 2 and the a-axis over the interval [-5, 5]. Find the area of…

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Q: Identify the radius and height. The region bounded by y x and the x-axis, -2 <x<1, revolved about x=…

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Q: Find the area of the region bounded by the graphs of y2 = 5 – x and y2 = 4x.   Please put a…

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Q: Find the area of the region described. The region bounded by y = /x, y = 2x- 15 and y = 0

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Q: (c) Calculate the area of a region bounded by the curves y = -x and y = -x, the line y = -3, and y =…

A: Given the curve y2=-x and y=-x2, the line y=-3 and y=2

Q: 3. Graph and then find the area of the region bounded by the curves y = 8x - x² and y=2x−7.

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Q: Sketch and find area of region: y=2x and y=5x^2.

A: We have to find the area of the region bounded by the curves y=2x and y=5x2.

Q: 3. Find the area of the region bounded by x = 3 – y and the line y = x – 1. Sketch the graph of the…

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Q: Find the area of the region bounded by y = 6-x-x² and the x-axis 125 6 (a) A = square units 6 (b) A=…

A: The given curves are; y=6-x-x2 and x-axis or y=0.   Now find the x-intercept of the the curve…

Q: Find the area of the given region. Use a graphing utility to verify your result. 1 + In(x³) y = y 1…

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Q: Sketch the region enclosed by the given curves. y-Vx-2, x- y- 2 y Find the area of the region.

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Q: a) Sketch and find the area of the region determined by the intersections of the curves. y = x² – 1,…

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.